Given: SR is the perpendicular bisector of QT; QR is the perpendicular bisector of SP
Prove: PQ=TS
Answers
Two lines are said to be perpendicular if they are at right angle to each other. The prove that PQ = TS is as stated below:
SR ⊥ QT (given)
QR ⊥ PS (given)
Comparing Δ PQS and ΔQST, we have:
Points Q and T are equidistant to bisector SR (bisection property of a line)
Points P and S are equidistant from QR (bisection property of a line)
QS is a common side to the triangles
Then,
PS ≅ QT (similar property of triangles)
Thus,
PQ ≅ ST (Side-Side-Side (SSS) property of triangles)
Therefore by Side-Side-Side (SSS) theorem, PQ = ST.
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Related Questions
To solve two-step equations, it is useful to use reverse ________________ as a guide to isolate the variable efficiently. *
Answers
Answer:
operations
Step-by-step explanation:
to solve two-step equations, it is useful to use reverse operations as a guide to isolate the variable efficiently.
Solve the equation by completing the
square. Enter the smallest solution first
and round to the nearest tenth.
s? - 8s - 4 = 0
-
s = [?]
Answers
Answer:
s ≈ - 0.5 , s ≈ 8.5
Step-by-step explanation:
s² - 8s - 4 = 0 ( add 4 to both sides )
s² - 8s = 4
To complete the square
add ( half the coefficient of the s- term )² to both sides
s² + 2(- 4)s + 16 = 4 + 16
(s - 4)² = 20 ( take square root of both sides )
s - 4 = ± [tex]\sqrt{20}[/tex] ( add 4 to both sides )
s = 4 ± [tex]\sqrt{20}[/tex]
Then
s = 4 - [tex]\sqrt{20}[/tex] ≈ - 0.5 ( to the nearest tenth ) ← smaller solution
s = 4 + [tex]\sqrt{20}[/tex] ≈ 8.5 ( to the nearest tenth ) ← larger solution
Write a proportion relating the side lengths of the triangle to any other triangle that has the line as a hypotenuse, a horizontal length of x units, and a vertical length of y units.
Answers
Answer:
y/x = 2 or y = 2xStep-by-step explanation:
The given triangle has:
Vertical segment = 2 unitsHorizontal segment = 1 unitThe ratio (slope) is:
2/1 = 2For any triangle using same line the proportion is:
y/x = 2 ory = 2xWhich list shows all the factors of 72?
A. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
B. 1, 2, 3, 4, 6, 9, 12, 18, 24, 36, 72
C. 1, 2, 3, 4, 5, 6, 8, 9, 12, 18, 24, 36, 72
D. 1, 2, 3, 4, 6, 7, 8, 9, 12, 18, 24, 36, 72
PLS HELPP :)
Answers
25. Save the simultaneous equations 2x-y=4;x+y=5
Answers
Answer:
Step-by-step explanation:
2x-y=4 ..........(1)
x+y=5 ...........(2)
Add equation 1 and 2:
We get:
3x=9
x=9/3
x=3
Substitute value of x in (2):
x+y=5
3+y=5
y=5-3
y=2
(3,2)
very time Luisa bakes a batch of brownies, she uses 12 cup of chocolate. If she has 32 cup(s) of chocolate remaining, how many batches of brownies can Luisa make? Input your answer as a whole number
Answers
Answer:
4
Step-by-step explanation:
Answer:she can make 4 batches of brownies
Step-by-step explanation:
since she already made a batch of brownie with 1/2 cup and she has 3/2 cups left, that means she can make 3 more
3+1=4
hope this helps
Step-by-step explanation:
Also try searching you question in brainly some of these questions are asked and answered
What is y=6-2x-4x^2+5x^3 in standard form?
Answers
In standard form is……
Y=5x^3-4x^2-2x+6
What is the solution set of the equation 6x^2 - 18x - 18 =6?
Answers
Answer:
The solution set is {4, -1}
Step-by-step explanation:
6x²- 18x -18 = 6
6x²- 18x -18 - 6 = 0
6x²- 18x -24 = 0
6(x² - 3x - 4) = 0
6(x - 4)(x + 1) = 0
6 = 0 not true
x - 4 = 0 ; x + 1 = 0
x = 4 x = - 1
The solution set is {4, -1}
!!!!!!!!!!!!!!!!!!!!!!!!!!!!5
Answers
can someone help me please
Answers
Answer:
a) interior angle: 156°
b) exterior angle: 24°
Step-by-step explanation:
b)The sum of the exterior angles of a convex polygon is 360°. Then the exterior angle of a regular 15-gon will be ...
360°/15 = 24°
__
a)The interior angle of a convex polygon is the supplement of the exterior angle at that vertex. For an exterior angle of 24°, a regular 15-gon will have an interior angle of ...
180° -24° = 156°
_____
Additional comment
We find it easier to work this problem by finding the exterior angle first. Note that the results only apply to a 15-gon in which all interior angles are congruent.
Solve for f.
1≤2–f
89 points pls help
Answers
Answer:
f ≤ 1
Step-by-step explanation:
1) Subtract 2 from both sides.
1 - 2 ≤ - f
2) Simplify 1 - 2 to - 1.
- 1 ≤ - f
3) Multiply both sides by - 1.
1 ≥ f
4) Switch Sides.
f ≤ 1
[tex]\\ \sf\longmapsto 1\leqslant 2-f[/tex]
Take 2 to right[tex]\\ \sf\longmapsto 1-2\leqslant -f[/tex]
[tex]\\ \sf\longmapsto -1\leqslant -f[/tex]
Multiply -1 on both sides
[tex]\\ \sf\longmapsto f\leqslant 1[/tex]
Write a conditional statement that represents the Euler Diagram.
If a plant is a _________ , then the plant is a _________.
Answers
Answer:
if a plant is a carrot , then the plant is a vegetable
Step-by-step explanation:
it just a grammar you should think
A 66-inch candle burns down in 12 hours. After how many hours will it have burned 5 3/4 inches?
Answers
Answer:
9.5 hours
Step-by-step explanation:
In the year 2000, the population of Florida was 16 million people. Since then, the population has grown at least 2% each year. How many years will it be before the state's population is at least 30 million people? Round to the nearest tenth of a year.
Answers
Using an exponential function, it is found that it will take 31.7 years for the state's population to be of at least 30 million people.
An increasing exponential function is given by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem:
The initial population is of 16 million people, hence [tex]A(0) = 16[/tex].The growth rate is of 2%, hence [tex]r = 0.02[/tex]Then:
[tex]A(t) = A(0)(1 + r)^t[/tex]
[tex]A(t) = 16(1 + 0.02)^t[/tex]
[tex]A(t) = 16(1.02)^t[/tex]
It will be 30 million after t years, for which A(t) = 30, hence:
[tex]A(t) = 16(1.02)^t[/tex]
[tex]30 = 16(1.02)^t[/tex]
[tex](1.02)^t = \frac{30}{16}[/tex]
[tex](1.02)^t = 1.875[/tex]
[tex]\log{(1.02)^t} = \log{1.875}[/tex]
[tex]t\log{1.02} = \log{1.875}[/tex]
[tex]t = \frac{\log{1.875}}{\log{1.02}}[/tex]
[tex]t = 31.7[/tex]
It will take 31.7 years for the state's population to be of at least 30 million people.
A similar problem is given at https://brainly.com/question/14773454
A wire bent in the form of a semi circle encloses an area of 7700cm2. If the same wire is bent into a square, calculate the area enclosed by the square
please hurry and answer fast..thank uuu so much
Answers
Answer: 8100 cm2
Step-by-step explanation:
First find radius
Area of semi circle = Pi*r2 / 2
7700 = 22/7 * r2/2
r2 = 7700 * 7 * 2 / 22
r2 = 700 * 7
r = square root of 7*7*10*10 ( I converted 700 into simpler numbers)
r = 7 x 10
r = 70 cm
Perimeter = r(Pi + 2)
= 70 ( 22/7 + 14/7)
= 70 * 36/7
= 360 cm
Let us take side of square as “x”
4x = 360
x = 360 / 4
x = 90
Area of square = side * side
= 90 * 90
= 8100 cm2
A semicircle is simply the half of a complete circle, and it can be gotten by dividing the circle through its center into equal halves.
The area of the enclosed square wire is 3025 square meters
The given parameters are:
[tex]\mathbf{Area= 7700cm^2}[/tex]
The area of a semicircle is
[tex]\mathbf{Area= \frac{\pi r^2}{2}}[/tex]
Substitute 7700 for Area
[tex]\mathbf{\frac{\pi r^2}{2} = 7700}[/tex]
Express pi as 22/7
[tex]\mathbf{\frac{22 \times r^2}{7 \times 2} = 7700}[/tex]
Divide through by 22
[tex]\mathbf{\frac{r^2}{7 \times 2} = 350}[/tex]
Multiply both sides by 14
[tex]\mathbf{r^2 = 4900}[/tex]
Take square roots of both sides
[tex]\mathbf{r = 70}[/tex]
Next, calculate the circumference of the semicircle
[tex]\mathbf{C = \pi r}[/tex]
So, we have:
[tex]\mathbf{C = \frac{22}{7} \times 70}[/tex]
[tex]\mathbf{C = 220}[/tex]
This means that the length of the wire is 220 meters.
This also represents the perimeter of the square.
The perimeter of the square is calculated using:
[tex]\mathbf{P = 4L}[/tex]
Where L represents the side length
So, we have:
[tex]\mathbf{4L = 220}[/tex]
Divide both sides by 4
[tex]\mathbf{L = 55}[/tex]
The area of the enclosed square is then calculated using:
[tex]\mathbf{Area = L^2}[/tex]
So, we have:
[tex]\mathbf{Area = 55^2}[/tex]
Evaluate the square
[tex]\mathbf{Area = 3025}[/tex]
Hence, the area of the enclosed square wire is 3025 square meters
Read more about areas at:
https://brainly.com/question/17091819
What is the quotient of 9198 and 14?
Answers
Answer:
656.36
Step-by-step explanation:
you just divide then have to round the decimal point to 36
What are the coordinates of point A?
o (5, 1)
(1, 5)
O (-1, 5)
Answers
Answer:
(1, 5)
Step-by-step explanation:
x is 1 to the right
y is 5 up
Therefor
(1, 5)
The ratio of red cars to blue cars in a parking lot was 9 : 7. If there were 72 red cars, how many blue cars were there?
Answers
Answer:
56
Step-by-step explanation:
We can mark the blue cars as x, so now, we have 9:7, and 72:x, we can use cross multiplication to get the value of x, 72*7 = 9x, which we can simplify into 504 = 9x, and can divide both sides by 9 to get 56 = x.
Hope it helped!
4(x + 3) + 3x = 24
Step by step please
Answers
Answer: 12/7
Step-by-step explanation: steps in pic, hope this helps!
At a school
Number of boys : number of girls 11:9
There are 124 boys than girls
Work out the total amount of students at the school
Answers
Step-by-step explanation:
Total ratio =11+9
=20
=120/20×124
=744
therefore the number of students are 744
What is the symbol for a square root
Answers
Answer:
The symbol for a square root is [tex]\sqrt{}[/tex].
:)
Answer:
√
Step-by-step explanation:
Math=Explanitory
It took 5 days for a committee of 7 pupils to clean the auditorium for the school program. How many days would have taken the committe of 10 pupils to do the same work?
Answers
Answer:
3.5 days
Step-by-step explanation:
If it takes 7 pupils 5 days, then it would take 1 pupil 7 times as long, or 35 days.
1 pupil alone cleans the auditorium is 35 days.
10 pupils work 10 times faster than 1 pupil, so 10 pupils take 3.5 days.
hurry please im dead meat if i cant do this picture below
Answers
Answer:
4 divided by 1/8
hope it helps
Step-by-step explanation:
Determine the measure∠d.
Answers
14°is the correct answer.
Please mark my answer as brainest and follow me to get the answer faster
Answer:
∡d = 83°
Step-by-step explanation:
∡d is 180 - 97 = 83°
∡d and the 97° angle are supplementary, meaning their sum is 180 degrees
Which relation is not a function?
A. {(2, 4), (1, 2), (0,0), (-1,2), (-2,4)}
B. {(2,4), (1, 1), (0,0), (-1, 1), (-2,4)}
C. {(2, 2), (1, 1), (0,0), (-1,1), (-2, 2)}
D. {(2, 2), (1, 1), (0,0), (1,-1), (2,-2)}
Answers
Answer: Choice D
Explanation:
We have the two points (2,2) and (2,-2) which have a repeated x coordinate. This is not allowed if we wanted a function. A function must have any x input lead to exactly one and only one output (assuming the input is in the domain).
Answer:
the correct is C. because they are lines going to 2.
A line goes through the points (8,11) and (-2,7). What is the slope of the line? Show your work. Write the equation of the line in point-slope form. Show your work. Write the equation of the line in slope-intercept form. Show your work.
Answers
Answer:
Step-by-step explanation:
Use matrices to rotate the vector v=<-4 , 1> by 270°. Write the resulting vector in component form
Answers
Using rotation rules, it is found that the resulting vector is:
v = <1, 4>
When a vector in component form <x,y> is rotated by 270 degrees, the rule is:
<x, y> -> <y, -x>
That is, x and y are switched, and the signal of x changes.
In this problem, the vector is v <-4, 1>, hence:
<-4, 1> -> <1, -(-4)> -> <1,4>
Hence, <1,4> is the resulting vector.
A similar problem is given at https://brainly.com/question/12673036
what single transformation rule would be the same as a reflection across y=5 and then across the line y=-2?
I know the answer is T(0,-14) but I don’t understand how it’s -14?
Answers
The total student at Shiloh middle school is 1,400 students. If the ratio of boy to girls is 3:4 for the school how many students are boys and how many students are girls
Answers
There are 600 boys and 800 girls.
SOLUTION:We are given the following facts:
The total number of students is 1,400.The ratio of boys to girls is 3:4.We express this as a partitive proportion.
» Solve for x.
[tex] \sf 3x + 4x = 1400 [/tex][tex] \sf 7x = 1400 [/tex][tex] \sf x = \frac{1400}{7} [/tex][tex] \sf x = 200 [/tex]Now we to solve for the number of boys and the number of girls.
» Number of boys:
= [tex] \sf 3x [/tex] = [tex] \sf (3)(200) [/tex] = [tex] {\boxed{\sf 600}} [/tex]» Number of girls:
= [tex] \sf 4x [/tex] = [tex] \sf (4)(200) [/tex] = [tex] {\boxed{\sf 800}} [/tex]Thus, there are 600 boys and 800 girls. The sum of these is the total number of students in Shiloh Middle School.
HOPE IT HELPS!16+16×5+7+7+7+7+7+7+7+7+7+7+7+7
Answers
Answer:
180
Step-by-step explanation:
[tex]16+16*5+7+7+7+7+7+7+7+7+7+7+7+7\\16+80+7+7+7+7+7+7+7+7+7+7+7+7\\16+80+84\\180[/tex]
Answer:
180
Step-by-step explanation: